1. Technical Field
The technical field of the invention is magnetic resonance imaging (MRI) in general, and more specifically: methods and algorithms for generating internal magnetic susceptibility distributions from complex-valued MR images (i.e., MR images containing complex numbers with magnitude and phase parts).
2. Introduction
In magnetic susceptibility tomography, the internal distribution of magnetic susceptibility of an object is determined by applying various configurations of magnetic fields and measuring how the object perturbs them. Measurement of the perturbed magnetic fields can be done using superconducting quantum interference devices (SQUID) called susceptometers or biosusceptometers. However, the present invention is directed to innovative computational techniques and software algorithms that analyze the data generated by magnetic resonance imaging (MRI) scanning machines (MRI scanners). In particular, the present invention primarily uses T2*-weighted images that are generated by MRI scanners using gradient-echo (GE) imaging sequences (also referred to as “T2*MRI”).
T2*MRI refers to the detection of transverse magnetization dephasing signal that is caused by a combination of spin-spin relaxation (T2 effect) and magnetic field inhomogeneity (T2′ effect) [1, 2]. As a noninvasive 3D imaging modality, the T2*MRI technology has been accepted for both structural iron deposit measurement in tissues and organs [3-9] and for brain functional neuroimaging [1, 10-13]. For general tissue structural imaging, the susceptibility source (dented by χ) is mainly attributed to the nonheme iron deposit therein; and for brain functional imaging, the total χ source consists of a neuron-induced heme iron perturbation (superimposed on the static structural susceptibility background), as described by the blood oxygenation level dependent (BOLD) physiological model [12, 14, 15].
In electromagnetism, it is understood that, when an entity of inhomogeneous susceptibility distribution is introduced into a main magnetic field, it will be magnetized through the material and magnetic field interaction mechanism [16]) and disturbs the field distribution by superimposing an inhomogeneous fieldmap on the main field. With the T2*MRI technology, that is a frequency spatial encoding and decoding scheme for multivoxel image acquisition through the applications of field gradients, we obtain a complex-valued MR image (consisting of a pair of magnitude and phase images), of which the MR magnitude is conventionally considered as an MR image of the χ source.
Magnetic susceptibility is the physical property controlling (driving) the T2*-weighted magnetic resonance imaging modality (T2*MRI). For medical imaging, T2*MRI is used to detect the magnetic susceptibility expression of a tissue or an organ state for quantitative iron measurement. It has been found that the output image of T2*MRI is not an exact representation of the susceptibility source (due to local average and nonlinearity associated with T2*MRI), thus not directly useful for iron measurement.
Based on MRI physics, we clarify that neither the MR magnitude image, not the MR phase image, is an exact tomographic reproduction of the susceptibility source or the fieldmap [17-19]. In particular, the MR magnitude image is a nonlinear transformation of the χ source, which may suffer from non-negativity and edge-effect pitfalls [19]; whereas the MR phase image is linearly related to the fieldmap in small angle regime(a linear phase approximation condition)[17, 19]. Due to the 3D convolution transformation during susceptibility magnetization [19, 20], it is not surprising to notice that the fieldmap (or phase image) appears morphologically different from the χ source: textural, noisy, and blurry. Therefore, in this invention, we strive to reconstruct the intact χ source from MR phase image.
The T2*MRI technology imposes a series of spatial transformations to the susceptibility source. Toward representing the entity in its intact χ distribution (by removing the transformations exerted by T2*MRI detection), the χ tomography is of paramount significance [19, 21-26].
The mainstay of existent publications on magnetic susceptibility mapping can be classified into three main kinds of solvers [17]. The first kind of solver is based on matrix inverse (for the exploitation of the well-established Tikhonov regularization techniques), which however is confronted with large matrix problem (dimensionality curse) because the 3D convolution imaging formula should be converted to 2D matrix-vector-multiplication format as required by matrix algebra [17, 27-31]. Limited to very small volume reconstruction, the report in [31] only deals with 4×4×4 multivoxel image, which is too small to be meaningful. In comparison, our susceptibility tomography technique in this report can easily accommodate a very large volume such as 512×512×512.
The second kind of solver is based on the 3D inverse filtering in 3D Fourier space [22, 25, 26, 32, 33]. This strategy suffers from stripe artifact and image energy shift problem. To deal with the pole singularity (infinites) on the 3D inverse filter, a truncation regularization is always used; hence called “filter truncation”. In presence of noise, the filter truncation solver will produce stripe or clutter artifacts. Furthermore, the energy of the filtered image will not be conserved due to the truncation on the inverse filter.
The third kind of solver is a 3D TV-regularized deconvolution method, which is used by preferred embodiments of the present invention to reconstruct a 3D χ source distribution from a 3D MR phase image[17, 19], as will be described later.